Towards Data-driven LQR with Koopmanizing Flows

TL;DR

This paper introduces a data-driven approach that learns finite-dimensional Koopman operator models for nonlinear systems, enabling efficient LQR control through a novel Koopmanizing Flows framework.

Contribution

It presents a new method extending Koopmanizing Flows to systems with control, allowing linear control design for nonlinear dynamics.

Findings

Demonstrates improved control performance in simulations

Learns meaningful lifting coordinates for nonlinear systems

Replaces nonlinear control with efficient LQR design

Abstract

We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional but, crucially, linear. To utilize it for efficient LTI control design, we learn a finite representation of the Koopman operator that is linear in controls while concurrently learning meaningful lifting coordinates. For the latter, we rely on Koopmanizing Flows - a diffeomorphism-based representation of Koopman operators and extend it to systems with linear control entry. With such a learned model, we can replace the nonlinear optimal control problem with quadratic cost to that of a linear quadratic regulator (LQR), facilitating efficacious optimal control for nonlinear systems. The superior control performance of the proposed method is demonstrated on simulation examples.